Only recycle if they are not rusty. Otherwise throw in trash.
Because of their size, blue bins are the best choice for metal caps & lids. Other recycling options are less advisable
There are sometimes (but rarely) collection drives for metal bottle caps.
Drives for plastic bottle caps are more common as they are more frequently collected for art projects and school activities.
If the metal is rusty, put it in the trash
Metal caps on bottles are typically used for carbonated drinks like beer and some brands of sparkling water.
They are magnetic so despite their small size, they are easily sorted at the material recovery facility (recycling sorting plant).
Jar lids are almost always steel and therefore magnetic. So they are also easy to recover at the sorting plant.